{"id":431,"date":"2017-03-15T19:42:02","date_gmt":"2017-03-15T19:42:02","guid":{"rendered":"http:\/\/pages.charlotte.edu\/colloquium\/?p=431"},"modified":"2017-03-27T00:31:08","modified_gmt":"2017-03-27T00:31:08","slug":"wednesday-march-20-330-430pm-fretwell-315","status":"publish","type":"post","link":"https:\/\/pages.charlotte.edu\/colloquium\/blog\/2017\/03\/15\/wednesday-march-20-330-430pm-fretwell-315\/","title":{"rendered":"Wednesday, March 29, 3:30-4:30PM, Fretwell 315"},"content":{"rendered":"<table>\n<tbody>\n<tr>\n<td>Zhiyi Zhang,\u00a0Department of Mathematics and Statistics,\u00a0University of North Carolina at Charlotte<\/td>\n<\/tr>\n<tr>\n<td>Title:<a style=\"font-family: inherit;font-size: inherit\" name=\"m_-6758539435527812225_OLE_LINK4\"><\/a>Statistical Implications of Turing\u2019s Formula<\/td>\n<\/tr>\n<tr>\n<td>\n<p>Abstract:<\/p>\n<p>This talk is organized into three parts.<\/p>\n<p>1. Turing\u2019s formula is introduced. Given an iid sample from an countable alphabet under a probability distribution, Turing\u2019s formula (introduced by Good (1953), hence also known as the Good-Turing formula) is a mind-bending non-parametric estimator of total probability associated with letters of the alphabet that are NOT represented in the sample. Many of its statistical properties were not clearly known for a stretch of nearly sixty years until recently. Some of the newly established results, including various asymptotic normal laws, are described.<\/p>\n<p>2. Turing\u2019s perspective is described. Turing\u2019s formula brought about a new perspective (or a new characterization) of probability distributions on general countable alphabets. The new perspective in turn provides a new way to do statistics on alphabets, where the usual statistical concepts associated with random variables (on the real line) no longer exist, for example, moments, tails, coefficients of correlation, characteristic functions don\u2019t exist on alphabets (a major challenge of modern data sciences). The new perspective, in the form of entropic basis, is introduced.<\/p>\n<p>3. Several applications are presented, including estimation of information entropy and diversity indices<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Zhiyi Zhang,\u00a0Department of Mathematics and Statistics,\u00a0University of North Carolina at Charlotte Title:Statistical Implications of Turing\u2019s Formula Abstract: This talk is organized into three parts. 1. Turing\u2019s formula is introduced. Given an iid sample from an countable alphabet under a probability distribution, Turing\u2019s formula (introduced by Good (1953), hence also known as the Good-Turing formula) is [&hellip;]<\/p>\n","protected":false},"author":333,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":true,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[1],"tags":[],"class_list":["post-431","post","type-post","status-publish","format-standard","hentry","category-spring-2022"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3kCtT-6X","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts\/431","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/users\/333"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/comments?post=431"}],"version-history":[{"count":4,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts\/431\/revisions"}],"predecessor-version":[{"id":435,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts\/431\/revisions\/435"}],"wp:attachment":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/media?parent=431"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/categories?post=431"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/tags?post=431"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}